Optimum Heat Power Cycles for Specified Boundary Conditions

Abstract

Optimization of the power output of Carnot and closed Brayton cycles is considered for both finite and infinite thermal capacitance rates of the external fluid streams. The method of Lagrange multipliers is used to solve for working fluid temperatures that yield maximum power. Analytical expressions for the maximum power and the cycle efficiency at maximum power are obtained. A comparison of the maximum power from the two cycles for the same boundary conditions, i.e., the same heat source/sink inlet temperatures, thermal capacitance rates, and heat exchanger conductances, shows that the Brayton cycle can produce more power than the Carnot cycle. This comparison illustrates that cycles exist that can produce more power than the Carnot cycle. The optimum heat power cycle, which will provide the upper limit of power obtained from any thermodynamic cycle for specified boundary conditions and heat exchanger conductances is considered. The optimum heat power cycle is identified by optimizing the sum of the power output from a sequence of Carnot cycles. The shape of the optimum heat power cycle, the power output, and corresponding efficiency are presented. The efficiency at maximum power of all cycles investigated in this study is found to be equal to (or well approximated by) η=1−TL,in/φTH,in where φ is a factor relating the entropy changes during heat rejection and heat addition.

Power Generation Targets from Hot Composite Curves

“…Later, Ondrechen et al [16] determined the power generation limit from a finite hot temperature reservoir and an isothermal cold temperature reservoir using an infinite number of parallel Carnot cycles. Ibrahim et al [17] and Park and Min [18] employed a similar approach to determine numerically the maximum theoretical efficiency for a system with both a finite hot temperature reservoir and a finite cold temperature reservoir. These methods did not consider power generation from multiple heat sources.…”

Optimal Thermodynamics—New Upperbounds

“…The most commonly-used way to account for the internal irreversibility of a machine (converter) is to introduce a cycle irreversibility ratio I according to [31] :…”

Performance Analysis and Optimization of a Solar Powered Stirling Engine with Heat Transfer Considerations

“…[5] showed that the production rate of entropy is greatly reduced by costing part of output power, when the optimum thermal efficiency is approximated as the average of the respective efficiency suggested by Carnot and that suggested by Curzon and Ahlborn [2]. In 1991, Ibrahim et al [6] considered irreversible parameters -the isentropic ratio of the isothermal processes and thus optimized the Carnot cycle by a more practical manner. Based on the assumption that the temperature of a gas varies linearly with the temperature of the surface of the wall of the cylinder that contains it, Klein [7] proposed the net output power and an optimized compression ratio for designing an engine with the greatest possible power output.…”